Improved edge-coloring with three colors

We show an O(1.344(n)) = O(2(0.427n)) algorithm for edge-coloring an n-vertex graph using three colors. Our algorithm uses polynomial space. This improves over the previous 0(2(n/2)) algorithm of Beigel and Eppstein [R. Beigel, D. Eppstein, 3-coloring in time O(1.3289n), J. Algorithms 54 (2) (2005) 168-204.]. We apply a very natural approach of generating inclusion-maximal matchings of the graph. The time complexity of our algorithm is estimated using the "measure and conquer" technique. (C) 2009 Elsevier B.V. All rights reserved.